Method and system for regulating the average electromagnetic torque of a rotating electrical machine, storage medium and data structure for carrying out the method

ABSTRACT

A method is described for regulating the average electromagnetic torque of a polyphase rotating electrical machine, supplied with a polyphase voltage and a polyphase current that are generated by an inverter. The method comprises a step of controlling the machine, using an exact response control process to do this, a step of determining the value of the harmonics of the voltage and/or the current which are generated by the inverter, and a step of calculating the instantaneous torque set point as a function of the value of the harmonics and an average torque set point, so as to produce an instantaneous torque set point suitable for limiting the difference between the average of the instantaneous electromagnetic torque, between two successive regulation times, and said average torque set point.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to a method and a system for regulating theaverage electromagnetic torque of a polyphase rotating electricalmachine equipped with stator and/or rotor windings. The invention alsorelates to storage media and a data structure for carrying out thismethod.

2. Description of the Prior Art

To be more precise, the invention relates to a method for regulating amachine in which the stator and/or rotor windings are supplied with apolyphase voltage and a polyphase current that are generated by aninverter, the inverter being formed by switches whose switching iscontrollable, this method including:

-   -   a control step of switching the switches as a function of an        instantaneous torque set point, using an exact response control        process to do this so that the instantaneous torque set point is        reached as soon as the next regulation time, and    -   a step at each regulation time of calculating, from an average        torque set point, the instantaneous torque set point to be        applied so that the average of the instantaneous electromagnetic        torque of the machine converges toward said average torque set        point.

In the remainder of the description, the term “motor” will be used todenote a polyphase rotating electrical machine, and the term “torque”will be used to denote the electromagnetic torque of this kind ofmachine.

The above methods have a very wide regulation dynamic range since theinstantaneous torque set point can be modified at each regulation time,and it is reached as soon as the next regulation time.

Such control methods are thus particularly useful for applications inwhich the torque set point changes abruptly. For example, these methodsare used to control drive motors of a rolling mill.

However, when the instantaneous torque set point is obtained by simpleequalization, for example by assimilating the average torque set pointwith the instantaneous torque set point, there is a difference betweenthe value of the average torque set point and the average of theinstantaneous torque between two successive regulation times. Theaverage torque set point is therefore either never reached perfectly, orit is reached by forming the average of the instantaneous torque over alarge number of regulation times, so that the method no longer has awide regulation dynamic range.

It is therefore an object of the invention to overcome this drawback byproviding a method for regulating the average electromagnetic torquewhich has a wide regulation dynamic range.

The invention therefore relates to a method for regulating the averageelectromagnetic torque as described above, which method includes a stepof determining the value of the harmonics of the voltage and/or thecurrent which are generated by the inverter, and the instantaneoustorque set point is also established during the calculation step as afunction of this value of the harmonics, so as to produce aninstantaneous torque set point suitable for limiting the differencebetween the average of the instantaneous electromagnetic torque, betweentwo successive regulation times, and said average torque set point.

It has been found that the difference between the average torque setpoint and the average of the instantaneous torque between two successiveregulation times is due to the fact that the inverter cannot generateperfectly sinusoidal voltages or currents from a direct current voltage.In reality, the voltage and the current that are generated are resolvedinto a sinusoidal component at a fundamental frequency and intosinusoidal components with higher frequencies, corresponding to theharmonics with an order greater than or equal to two. The fundamentalfrequency sinusoidal component is simply referred to here as thefundamental, whereas the higher frequency sinusoidal components arereferred to as harmonics.

The fundamental creates a constant torque Γ_(m) over a fundamentalperiod. The harmonics generate an oscillating secondary torque with ahigher frequency. The instantaneous torque Γ_(s) of the motor is theresult of superposition of the torque Γ_(m) and the oscillating torque.The oscillating torque and the torque Γ_(m) are mutually independent.The known methods, which calculate an instantaneous torque set pointonly as a function of the average torque set point, do not thereforetake the oscillating torque into account. Even if, for example, theinstantaneous torque at each regulation time is strictly identical tothe average torque set point, the average of the instantaneous torqueΓ_(s) between two successive regulation times will therefore not beequal to this average torque set point, since the instantaneous torquevaries between these two times owing to the oscillating torque. Theoscillating torque is therefore responsible for the difference betweenthe average torque set point and the average of the instantaneoustorque. This difference increases commensurately when the amplitude ofthe oscillating torque is large. Since the oscillating torque is createdby voltage and/or current harmonics, the value of this difference istherefore a function of the value of the harmonics.

The above method corrects the deficiency of the known methods by takinginto account not only the average torque set point, but also the valueof the current and/or voltage harmonics, for calculating theinstantaneous torque set point.

SUMMARY OF THE INVENTION

According to other characteristics of the method according to theinvention, it is distinguished as follows:

-   -   the exact response control process establishes a set point for        controlling the switches by pulse width modulation, and the        control step also includes a control operation of switching the        switches between each regulation time, employing a pulse width        modulation process configured as a function of said control set        point established by the exact response control process;    -   the pulse width modulation process is a pulse width modulation        process synchronous with the frequency of the fundamental of the        voltage generated by the inverter, and the regulation times are        spaced apart by a time interval equal to T′/2p, where p is the        number of phases of the machine and T′ is the period of the        fundamental of the voltage generated by the inverter;    -   the exact response control process is adapted so that the phase        of the fundamental of the voltage generated by the inverter at        the regulation times is equal to $\frac{k\quad\pi}{p},$        k being an integer;    -   the value of the harmonics is established, during the        determination step, from the value of the control set point        established by the exact response control process at the        preceding regulation time;    -   the pulse width modulation process successively uses a plurality        of different pulse width modulations over time; the value of the        harmonics is established from at least one calculation        parameter, the various values of the or each parameter being        calculated in advance and prerecorded for each different pulse        width modulation liable to be used; and the value of the or each        parameter to be used during the determination step is selected        as a function of the value of the control set point established        by the exact response control process at the preceding        regulation time;    -   a calculation parameter is defined by the following        relationship:        ${ɛ(0)} = \left( {\sum\limits_{n = 2}^{\infty}\quad\frac{V_{n}}{n}} \right)_{0}$    -   where:    -   V_(n) is the amplitude of the voltage harmonic of order n,    -   n is an integer corresponding to the order of the harmonic;    -   the control set point is a voltage vector defined, in an        orthonormal reference frame α,β which is fixed with respect to        the stator windings, by its modulus and an angle, and in that        the value of the current harmonics is established from the        following relationship:        ${\Delta\quad I_{q}} = {{- \frac{ɛ(0)}{L \cdot \omega}} \cdot {\cos\left( {\beta_{0} - \rho_{0}} \right)}}$    -   where:    -   L is the stator inductance of the rotating electrical machine,    -   ω is the angular velocity of the rotor of the rotating        electrical machine,    -   β₀ is the angle of the voltage vector established (at 96) at the        preceding regulation time by the exact response control process,    -   ΔI_(q) is the value of the current harmonics along the axis q in        a rotating reference frame d,q associated with the rotor flux,        the rotor flux being aligned with the axis d, and    -   ρ₀ is the angle of the reference frame d,q with respect to the        fixed reference frame α,β associated with the stator windings.    -   a calculation parameter is defined by the following        relationship:        ${\delta(0)} = \left( {\sum\limits_{n = 2}^{\infty}\quad V_{n}} \right)$    -   where Vn is the amplitude of the voltage harmonic of order n;    -   the inverter is supplied from at least one amplitude-limited        direct current supply voltage, and the instantaneous torque set        point is also established during the calculation step as a        function of the instantaneous value of the direct current        voltage available at the regulation time, so that the        instantaneous torque set point corresponds to an available        direct current voltage.    -   the instantaneous torque set point is established in the form of        an instantaneous current set point with the aid of the following        relationships: $\begin{matrix}        {{\left\lbrack {{\hat{I}}_{d} - {\hat{I}}_{d\quad c}} \right\rbrack^{2} + \left\lbrack {{\hat{I}}_{q} - {\hat{I}}_{q\quad c}} \right\rbrack^{2}} \leq \frac{{\hat{V}}_{M}^{2}}{Z^{2}}} \\        {{{\hat{I}}_{d}^{2} + {\hat{I}}_{q}^{2}} \leq {\hat{I}}_{M}^{2}}        \end{matrix}$    -   where:    -   {circumflex over (V)}_(M) is the instantaneous value of the        maximum direct current voltage available for supplying the        inverter,    -   Î_(M) is the instantaneous value of the maximum current that can        be generated by the inverter 8,    -   Î_(q) and Î_(d) are the components of the set point of the        instantaneous current vector respectively along the axes q and d        of the reference frame d,q    -   Z is defined by the following relationship:    -   Z={square root}{square root over (R²+L²·ω²)}, where R is the        stator resistance of the machine, L is the stator inductance of        the machine and ω is the angular velocity of the rotor of the        machine,    -   Î_(dc) and Î_(qc) are defined by the following relationships:        $\begin{matrix}        {{\hat{I}}_{d\quad c} = {{- \frac{L \cdot \omega}{Z^{2}}} \cdot \left\{ {{R \cdot \left( {{\Delta\quad I_{q}} - {\Delta\quad J_{q}}} \right)} - {L \cdot \omega \cdot \left( {{\Delta\quad I_{d}} - {\Delta\quad J_{d}}} \right)} + {\omega \cdot \Phi_{a}}} \right\}}} \\        {{\hat{I}}_{q\quad c} = {{- \frac{1}{Z^{2}}} \cdot \left\{ {{R \cdot \omega \cdot \phi_{a}} - {R \cdot L \cdot \omega \cdot \left( {{\Delta\quad I_{d}} - {\Delta\quad J_{d}}} \right)} - {L^{2} \cdot \omega^{2} \cdot \left( {{\Delta\quad I_{q}} - {\Delta\quad J_{q}}} \right)}} \right\}}}        \end{matrix}$    -   where:    -   ΔI_(d) and ΔI_(q) are the components of the harmonic current        vector generated by the inverter, respectively along the axes d        and q of the reference frame d,q, and ΔJ_(q) and ΔJ_(d) are        components proportional to the harmonic voltage vector generated        by the inverter, respectively along the axes q and d of the        reference frame d,q, the components ΔI_(d), ΔJ_(q) and ΔJ_(d)        being defined by the following relationships: $\begin{matrix}        {{\Delta\quad I_{d}} = {{+ \frac{ɛ(0)}{L \cdot \omega}} \cdot {\sin\left( {\beta_{0} - \rho_{0}} \right)}}} \\        {{\Delta\quad J_{d}} = {\frac{\delta(0)}{L \cdot \omega} \cdot {\sin\left( {\beta_{0} - \rho_{0}} \right)}}} \\        {{\Delta\quad J_{q}} = {{- \frac{\delta(0)}{L \cdot \omega}} \cdot {\cos\left( {\beta_{0} - \rho_{0}} \right)}}}        \end{matrix}$

The invention also relates to an information storage medium, whichincludes instructions for carrying out a regulation method according tothe invention, when these instructions are carried out by an electroniccomputer.

The invention also relates to a data structure which associates aplurality of angles and the value of at least one regulation parameterwith each particular value of a control set point established by theexact response control process, the set of angles associated with agiven value of said control set point defining a particular pulse widthmodulation synchronous with the frequency of the fundamental of thevoltage generated by the inverter, and the value of said at least oneregulation parameter being a function of the value of the current and/orvoltage harmonics which are generated by the inverter, when it iscontrolled with the aid of the pulse width modulation defined by theangles associated with the same value of the control set point.

The invention also relates to a system for regulating the averageelectromagnetic torque of a polyphase rotating electrical machineequipped with stator and/or rotor windings, which are supplied with apolyphase voltage and a polyphase current that are generated by aninverter, the inverter being formed by switches whose switching iscontrollable, this system including:

-   -   a control unit for the switching of the switches as a function        of an instantaneous torque set point, this control unit being        capable of using an exact response control process to do this so        that the instantaneous torque set point is reached as soon as        the next regulation time;    -   a unit for calculating, from an average torque set point, the        instantaneous torque set point to be applied so that the average        of the instantaneous electromagnetic torque of the machine        converges toward said average torque set point;    -   which system includes a unit for determining the value of the        harmonics of the voltage and/or the current which are generated        by the inverter, and wherein the calculation unit also        calculates the instantaneous torque set point as a function of        this value of the harmonics, so as to produce an instantaneous        torque set point suitable for limiting the difference between        the average of the instantaneous electromagnetic torque, between        two successive regulation times, and said average torque set        point.

The invention will be understood more clearly by reading the followingdescription, which is provided solely by way of example only and givenwith reference to the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of a regulation system according tothe invention.

FIG. 2 is graph representing the development of a control signalgenerated by the system in FIG. 1 as a function of time.

FIG. 3 is a flow chart of a regulation method according to theinvention.

FIG. 4 is graph representing the variation of the instantaneous torqueas a function of time, in the case of the regulation method in FIG. 3.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

FIG. 1 represents a system 2 for regulating the average electromagnetictorque of a motor 4 equipped with a stator and a rotor.

The remainder of the description will refer to the particular case inwhich this motor 4 is a smooth pole three-phase synchronous motor withpermanent magnets mounted at the surface of the rotor. The stator isequipped with stator windings.

In particular, the mathematical relationships given in the remainder ofthis description are those established from the equations of state ofthis kind of motor.

The system 2 is capable of receiving an average torque set point Γ_(cm)at its input and of delivering control signals for a conventionalthree-phase inverter 8 at its output. This inverter 8 is supplied by adirect current voltage source 10.

This inverter 8 conventionally comprises three branches known as “legs”,each formed by two switches connected in series by means of a centerpoint. The center point of each leg is connected to the stator windingsof the motor 4 so as to supply each phase of this motor with voltage andcurrent.

The system 2 includes a unit 20 for controlling the inverter 8 as afunction of an instantaneous torque set point, and a unit 22 forcalculating this instantaneous torque set point as a function of the setpoint Γ_(cm).

The control unit 20 includes an exact response control module 24, and amodule 26 for controlling the switching of the switches of the inverter8 by pulse width modulation.

The module 24 receives an instantaneous torque set point in the form aninstantaneous current vector (Î_(d), Î_(q)) at its input, and delivers avoltage vector {right arrow over (V)} at its output.

The instantaneous current vector (Î_(d), Î_(q)) is defined in a rotatingorthonormal reference frame d,q associated with the flux of the rotor ofthe motor 4, whose axis d is aligned with the rotor flux of the motorand whose axis q is derived from the axis d by a rotation through$\frac{\pi}{2}$in the right-handed trigonometric sense. The voltage vector {right arrowover (V)} is defined, in a fixed orthonormal reference frame α,βassociated with the stator of the motor 4, by its modulus ∥{right arrowover (V)}∥ and an angle β₀ with respect to the axis α. The referenceframes d,q and α,β are conventional in this technical field, andtransformation of the coordinates expressed in one reference frame intothose expressed in the other reference frame is carried out by rotatingthe reference axes.

To be more precise, the module 24 delivers the angle β₀ and the averageof the modulus of the voltage vector {right arrow over (V)}, between tworegulation times, at its output.

The angle β₀ is transmitted directly to an input of the control module26, whereas the modulus ∥{right arrow over (V)}∥ is transmitted to amodule 28 for selecting the type of pulse width modulation.

The module 24 is capable of calculating the value of the voltage vector{right arrow over (V)} so that the instantaneous torque set pointcorresponding to the set point (Î_(d), Î_(q)) is reached at the nextregulation time. To this end, the module 24 uses an exact responsecontrol process, also known as “deadbeat control”. For example, theprocess used here is described in patent application EP-A-123 35 06. Itwill therefore merely be mentioned as a reminder that the relationshipused to calculate the value of the voltage vector {right arrow over (V)}as a function of the input set point (Î_(d), Î_(q)) is as follows:$\begin{matrix}{V_{dq} = {{\begin{matrix}V_{d} \\V_{q}\end{matrix}} = {\frac{1}{a(T)} \cdot {\begin{matrix}{{\hat{I}}_{d} - {I_{d}^{0}(T)}} \\{{\hat{I}}_{q} - {I_{q}^{0}(T)}}\end{matrix}}}}} & (1)\end{matrix}$

-   -   in which: $\begin{matrix}        {{a(T)} = {\frac{1}{R} \cdot \left( {1 - {\mathbb{e}}^{- \frac{T}{\tau}}} \right)}} \\        {{and}\text{:}} \\        {\begin{matrix}        {I_{d}^{0}(T)} \\        {I_{q}^{0}(T)}        \end{matrix}}        \end{matrix}.$    -   is the natural development of the instantaneous currents of the        stator of the motor in short-circuit after a regulation interval        T, starting from the original state of the stator current at the        preceding measurement and regulation time for the currents.

T is the time interval between the current regulation time and the nextregulation time, R is the stator resistance of the motor, L is thestator inductance of the motor, and τ is the stator time constant$\left( {\tau = \frac{L}{R}} \right).$

The module 26 can control the switching of the switches of the inverter8 as a function of the value of the angle β₀ calculated by the module24, and as a function of the value of angles α_(i) selected by themodule 28. To this end, the module 26 uses a conventional pulse widthmodulation process synchronous with the frequency of the fundamental ofthe voltage generated by the inverter 8. An example of a control signalgenerated by this module 26 is represented in FIG. 2.

FIG. 2 represents the development of the signal for controlling an upperswitch of one leg of the inverter 8 as a function of time. Here, forexample, the value 0 of the signal indicates that the switch is to beopened and the value 1 indicates that the switch is to be closed. FIG. 2represents the regulation times as a function of the phase of thevoltage fundamental generated by the inverter 8. The interval [0, 2π] isdivided into four equal sub-intervals π₁, π₂, π₃ and π₄. In the intervalπ₁, the switching times of the switch are defined by angles α_(i). Here,seven angles α_(i) are needed to define the switching of the switchduring the interval π₁, and the pulse width modulation represented hereis therefore referred to as “seven-angled”. The switching times in theintervals π₂ to π₄ are derived by conventional transformations fromthose defined for the interval π₁. The control signals of the otherswitches are derived from that in FIG. 2 by shifting the signal of FIG.2 by $\frac{2\quad\pi}{p},$where p is the number of phases of the motor 4.

So as to eliminate the harmonics of even order and the harmonics whoseorder is a multiple of three, the control signal in this case has twoaxes of symmetry at the abscissas $\frac{\pi}{2}$and $\frac{3\quad\pi}{2},$and a point of symmetry P at the abscissa π.

A type of modulation is thus defined once the value of the angles α_(i)is known. The value of the angles α_(i) fixes the modulus of thefundamental of the voltage generated by the inverter.

The module 28 can select the value of the angles α_(i) which correspondto voltage moduli ∥{right arrow over (V)}∥. To this end, the module 28is associated with a memory 32 containing a table TP of the followingform: $\quad\begin{matrix}{\overset{\overset{\_}{->}}{V}}_{1} & {ɛ(0)}_{1} & {\delta(0)}_{1} & \alpha_{11} & \alpha_{21} & \alpha_{31} & \alpha_{41} & \alpha_{51} & \alpha_{61} & \alpha_{71} \\\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\{\overset{\overset{\_}{->}}{V}}_{k} & {ɛ(0)}_{k} & {\delta(0)}_{k} & \alpha_{1k} & \alpha_{2k} & \alpha_{3k} & \alpha_{4k} & \alpha_{5k} & \alpha_{6k} & \alpha_{7k} \\\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\{\overset{\overset{\_}{->}}{V}}_{m} & {ɛ(0)}_{m} & {\delta(0)}_{m} & \alpha_{1m} & \alpha_{2m} & \alpha_{3m} & \alpha_{4m} & \alpha_{5m} & \alpha_{6m} & \alpha_{7m}\end{matrix}$

For each normalized value ${\overset{\overset{\_}{->}}{V}}_{j}$of the voltage modulus ∥{right arrow over (V)}∥, this table provides thevalue of the angles α_(ik) allowing the inverter 8 to generate a voltagefor which the modulus of the fundamental is equal to the modulus ∥{rightarrow over (V)}∥. The relationship for converting from the normalizedvalue of the modulus ∥{right arrow over (V)}∥ to the value produced bythe module 24 is as follows:∥{right arrow over (V)}∥=∥{right arrow over (V)}∥·{circumflex over (V)}_(M)

-   -   where:    -   {circumflex over (V)}_(M) is the instantaneous value of the        voltage across the terminals of the source 10.

For each normalized value of the modulus ∥{right arrow over (V)}∥, thistable also provides the value of two parameters ε(0) and δ(0). The wayin which the values of these parameters are calculated, and theadvantage of using them, will become apparent on reading the remainderof the description. The modulus 28 can therefore select the value of theparameters ε(0) and δ(0) corresponding to the value of the modulus∥{right arrow over (V)}∥ and deliver them at its output.

If the normalized value ∥{right arrow over (V)}∥ lies between two valuesprerecorded in the table TP, the selection module 28 is able tocalculate the corresponding values of the parameters ε(0) and δ(0) andof the angles α_(i) by linear interpolation.

The control unit 20 also includes a module 30 for determining theregulation times. This module 30 can determine the interval T betweentwo successive regulation times so that it is equal to$\frac{T^{\prime}}{2p},$where T′ is the period of the fundamental of the voltage generated bythe inverter 8 and p is the number of phases of the motor 4. The reasonis that this choice of the value of the interval T has been found toeliminate certain orders of voltage harmonics generated by the inverter8. Furthermore, in order to simplify some of the relationships describedbelow, these regulation times are determined here in order to correspondto times at which the phase of the voltage vector {right arrow over (V)}is an integer multiple of $\frac{\pi}{p}.$To this end, for example, the module 30 can solve the followingrelationship by successive iterations so as to determine the value ofthe time interval T: $\begin{matrix}\begin{matrix}{{\sin\left\lbrack {{k \cdot \frac{\pi}{3}} - \left( {\rho_{0} + {\omega \cdot T} + \varphi_{D}} \right)} \right\rbrack} = {{\mathbb{e}}^{\frac{T}{\tau}} \cdot \frac{{{\overset{->}{I}}_{dq}^{D}(0)}}{{{\overset{->}{I}}_{dq}^{D}(T)}} \cdot}} \\{\sin\left( {{k \cdot \frac{\pi}{3}} - \left( {\rho_{0} + \varphi_{0}} \right)} \right)}\end{matrix} & (2)\end{matrix}$

-   -   where:    -   the angles φ_(D) and φ₀ are defined by the following        relationships: $\begin{matrix}        {{{\cos\left( \varphi_{D} \right)} = {{\frac{I_{d}^{D}(T)}{{{\overset{->}{I}}_{dq}^{D}(T)}}\quad{\cos\left( \varphi_{0} \right)}} = \frac{I_{d}^{D}(0)}{{{\overset{->}{I}}_{dq}^{D}(0)}}}}{{\sin\left( \varphi_{D} \right)} = {{\frac{I_{q}^{D}(T)}{{{\overset{->}{I}}_{dq}^{D}(T)}}\quad{\sin\left( \varphi_{0} \right)}} = \frac{I_{d}^{D}(0)}{{{\overset{->}{I}}_{dq}^{D}(0)}}}}} & (3)        \end{matrix}$    -   I_(d) ^(D)(T), I_(q) ^(D)(T), I_(d) ^(D)(0) and I_(q) ^(D)(0)        are defined by the following relationships: $\begin{matrix}        {{{{\overset{->}{I}}_{dq}^{D}(T)} = {{\begin{matrix}        {I_{d}^{D}(T)} \\        {I_{q}^{D}(T)}        \end{matrix}} = {\begin{matrix}        {{\hat{I}}_{d} + {\frac{X^{2}}{L \cdot Z^{2}} \cdot \Phi_{a}}} \\        {{\hat{I}}_{q} + {\frac{R \cdot X}{L \cdot Z^{2}} \cdot \Phi_{a}}}        \end{matrix}}}}{{{\overset{->}{I}}_{dq}^{D}(0)} = {{\begin{matrix}        {I_{d}^{D}(0)} \\        {I_{q}^{D}(0)}        \end{matrix}} = {\begin{matrix}        {{{\hat{I}}_{d}(0)} + {\frac{X^{2}}{L \cdot Z^{2}} \cdot \Phi_{a}}} \\        {{{\hat{I}}_{q}(0)} + {\frac{R \cdot X}{L \cdot Z^{2}} \cdot \Phi_{a}}}        \end{matrix}}}}} & (4)        \end{matrix}$    -   Where:    -   Φ_(a) is the rotor flux of the magnets,    -   L is the stator inductance of the motor,    -   X is defined by the relationship X=L.ω, where ω is the angular        velocity of the rotor,    -   Z is defined by the following relationship        Z ² =R ² +L ²·{overscore (ω)}²    -   Î_(d)(0) and Î_(q)(0) are the components in the reference frame        d,q of the instantaneous current vector measured at the current        regulation time,    -   Î_(d) and Î_(q) is the current set point received at the input        of the module 24.

Relationship (2) is obtained by solving the system of equations (1)supplemented by an extra equation in order to express the constraintaccording to which the phase of the voltage vector must be equal to$\frac{k\quad\pi}{p},$where k is an integer lying between [1, . . . ,6] and p is the number ofphases of the motor 4. In the three-phase case, this extra equation isfor example as follows: $\begin{matrix}{{{V_{\alpha} \cdot {\sin\left( {k \cdot \frac{\pi}{3}} \right)}} - {V_{\beta} \cdot {\cos\left( {k \cdot \frac{\pi}{3}} \right)}}} = 0} & (4)\end{matrix}$

-   -   where V_(α), V_(β) are the components of the voltage vector in        the reference frame α,β.

Further details about how to determine the time interval T may be foundin the French patent application entitled “Method for regulating theinstantaneous electromagnetic torque of a polyphase rotating electricalmachine” filed in France on the same day by the Applicant.

The calculation unit 22 converts the average torque set point Γ_(cm)into an instantaneous torque set point expressed in the form of theinstantaneous current vector set point (Î_(d), Î_(q)). To this end, itincludes a module 40 for calculating a fundamental current set pointĨ_(q) a module 42 for correcting this fundamental current set point anda module 44 for establishing the set point (Î_(d), Î_(q)) while takingthe operational limitations of the inverter 8 into account.

The module 40 establishes the fundamental current set point Ĩ_(q) fromthe set point Γ_(cm) with the aid of the following relationship:${\overset{\sim}{I}}_{q} = \frac{\Gamma_{cm}}{N_{p} \cdot \Phi_{a}}$

-   -   where:    -   N_(p) is the number of pole pairs of the motor,    -   Φ_(a) is the rotor flux of the magnets.

These two parameters N_(p) and Φ_(a) are known parameters which dependon the characteristics of the motor 4.

The module 42 can correct the set point Ĩ_(q) as a function of the valueof the harmonics of the current which is generated by the inverter 8,with the aid of the following relationship:Î _(q) =Ĩ _(q) +ΔI _(q)  (5)

-   -   where:    -   Î_(q) is the component of the set point (Î_(d), Î_(q)) along the        axis q of the reference frame d,q, and    -   ΔI_(q) is the component of the harmonic current vector along the        axis q of the reference frame d,q.

The harmonic current vector is the one corresponding only to theharmonics of the current which is generated by the inverter 8, withouttaking the fundamental into account.

The module 44 can establish the set point (Î_(d), Î_(q)) intended forthe module 24, which complies with the voltage and current limitationsof the inverter 8. To this end, the module 44 can solve the followingsystem of in equations: $\begin{matrix}{{\left\lbrack {{\hat{I}}_{d} - {\hat{I}}_{dc}} \right\rbrack^{2} + \left\lbrack {{\hat{I}}_{q} - {\hat{I}}_{qc}} \right\rbrack^{2}} \leq \frac{{\hat{V}}_{M}^{2}}{Z^{2}}} & (6) \\{{{\hat{I}}_{d}^{2} + {\hat{I}}_{q}^{2}} \leq {\hat{I}}_{M}^{2}} & (7)\end{matrix}$

-   -   where:    -   {circumflex over (V)}_(M) is the instantaneous value of the        maximum direct current voltage available across the terminals of        the source 10,    -   Î_(M) is the instantaneous value of the maximum current that can        be generated by the inverter 8,    -   Î_(d) is the component of the instantaneous current vector along        the axis d of the reference frame d,q    -   Z is defined by the following relationship:        Z={square root}{square root over (R ² +L ² ·ω ² )}    -   where R is the stator resistance, L is the stator inductance and        ω is the angular velocity.

Î_(dc) and Î_(qc) are defined by the following relationships:$\begin{matrix}{{\hat{I}}_{dc} = {{- \frac{L \cdot \omega}{Z^{2}}} \cdot \left\{ {{R \cdot \left( {{\Delta\quad I_{q}} - {\Delta\quad J_{q}}} \right)} - {L \cdot \omega \cdot \left( {{\Delta\quad I_{d}} - {\Delta\quad J_{d}}} \right)} + {\omega \cdot \Phi_{a}}} \right\}}} & (8) \\\begin{matrix}{{\hat{I}}_{qc} = {{- \frac{1}{Z^{2}}} \cdot \left\{ {{R \cdot \omega \cdot \phi_{a}} - {R \cdot L \cdot \omega \cdot \left( {{\Delta\quad I_{q}} - {\Delta\quad J_{q}}} \right)} - {L^{2} \cdot \omega^{2} \cdot}} \right.}} \\\left. \left( {{\Delta\quad I_{d}} - {\Delta\quad J_{d}}} \right) \right\}\end{matrix} & (9)\end{matrix}$

-   -   where:    -   ΔI_(d) is the component of the harmonic current vector along the        axis d of the reference frame d,q, and    -   ΔJ_(q) and ΔJ_(d) are components proportional to the harmonic        voltage vectors, respectively along the axes d and q of the        reference frame d,q.

Here, the instantaneous maximum voltage {circumflex over (V)}_(M) andthe angular velocity ω are measured. The instantaneous maximum currentÎ_(M) is constant and known from the electrical characteristics of theinverter 8. The calculation of the value of the components ΔI_(d),ΔJ_(q) and ΔJ_(d) is defined below.

The system 2 also includes a unit 50 for determining the harmonicvoltage and current vectors along the axes d and q of the referenceframe d,q. To this end, the unit 50 includes a first module 52 fordetermining the harmonic current vector and a second module 54 fordetermining the harmonic voltage vector. To be more precise, the module52 can deliver the value of the components ΔI_(q) and ΔI_(d) to themodules 42 and 44, and the module 54 can deliver the value of thecomponents ΔJ_(q) and ΔJ_(d) to the module 44.

To this end, the module 52 establishes the value of the componentsΔI_(q) and ΔI_(d) with the aid of the following relationships:$\begin{matrix}{{\Delta\quad I_{d}} = {\frac{ɛ(0)}{L \cdot \omega} \cdot {\sin\left( {\beta_{0} - \rho_{0}} \right)}}} & (10) \\{{\Delta\quad I_{q}} = {{- \frac{ɛ(0)}{L \cdot \omega}} \cdot {\cos\left( {\beta_{0} - \rho_{0}} \right)}}} & (11)\end{matrix}$

-   -   where:    -   ρ₀ is the angle of the reference frame d,q with respect to the        reference frame a,d fixed to the stator, and    -   β₀ is the angle of the vector {right arrow over (V)}.

The module 54 establishes the components ΔJ_(q) and ΔJ_(d) with the aidof the following formulae: $\begin{matrix}{{\Delta\quad J_{d}} = {\frac{\delta(0)}{L \cdot \omega} \cdot {\sin\left( {\beta_{0} - \rho_{0}} \right)}}} & (12) \\{{\Delta\quad J_{q}} = {{- \frac{\delta(0)}{L \cdot \omega}} \cdot {\cos\left( {\beta_{0} - \rho_{0}} \right)}}} & (13)\end{matrix}$

The modules 52 and 54 are also connected to the outputs of the module 24and of the module 28, so as to obtain the value of the angle β₀ and thevalue of the parameters ε(0) and δ(0).

ΔI_(q) and ΔI_(d) are associated with the values of the voltageharmonics by the following relationships $\quad\left\{ \begin{matrix}{{\Delta\quad V_{d}} = {L\quad\omega\quad\Delta\quad J_{d}}} \\{{\Delta\quad V_{q}} = {L\quad\omega\quad\Delta\quad J_{q}}}\end{matrix} \right.$

-   -   Where:    -   and ΔV_(q) and ΔV_(d) are the components of the harmonic voltage        vector, respectively along the axes q and d of the reference        frame d,q.

However, only the components ΔJ_(d) and ΔJ_(q) are used here.

Lastly, the system 2 includes a sensor 56 for the angular position ρ₀ ofthe rotor of the motor 4, a sensor 58 for the angular velocity co of therotor of the motor 4, a sensor 60 for the instantaneous direct currentvoltage {circumflex over (V)}_(M) delivered by the source 10 to theinverter 8, and a sensor 62 for the instantaneous current in the statorwindings.

The sensor 62 is formed by a plurality of elementary-current sensors,each suitable for measuring the current in the stator windings of onephase of the motor 4, so as to measure the instantaneous current vector.This sensor 62 can also convert the measured instantaneous currentvector using the generalized Concordia transformation for a polyphasesystem, so as to deliver the two components of the instantaneous currentvector Î_(d)(0) and Î_(q)(0) directly at its output.

These sensors are connected to the various modules which require ameasurement of these values. In particular, the sensor 56 delivers thevalue of the angle ρ₀ to the modules 52 and 54. The connections betweenthe sensors 56 to 62 and the various modules of the system 2 have notall been represented in order to simplify the illustration.

The system 2 is typically produced with the aid of conventionalprogrammable electronic computers. To this end, the system 2 isassociated with a memory 61 containing instructions for carrying out themethod of FIG. 3, when these are carried out by the system 2.

The way in which the system 2 operates will now be described withreference to the method of FIG. 3.

The method of FIG. 3 is broken down into two main phases, a phase 80 ofinitializing the various constant parameters used by the modules of thesystem 2, and a phase 82 of regulating the torque of the motor 4.

During the phase 80, the values of the parameters Np, Φ_(a), Î_(M), R, Land Z are determined from the electrical and mechanical characteristicsof the motor and of the inverter 8. Once determined, for example, theseparameter values are stored in the memory 61.

During the phase 80, the values of the parameters ε(0) and δ(0) aredetermined for each value of the modulus ∥{right arrow over (V)}∥ withthe aid of the following relationships: $\begin{matrix}{{ɛ(0)} = \left( {\sum\limits_{n = 2}^{\infty}\frac{V_{n}}{n}} \right)_{0}} & (14) \\{{\delta(0)} = \left( {\sum\limits_{n = 2}^{\infty}V_{n}} \right)} & (15)\end{matrix}$

-   -   where:    -   V_(n) is the amplitude of the harmonic of order n, and    -   n is an integer corresponding to the order of the harmonic.

The amplitude of the harmonics varies as a function of the type ofmodulation, that is to say as a function of the value of the anglesα_(i) and of the instantaneous value of the direct current voltage.

The relationships were established for the case in which the regulationtimes are selected to correspond exactly with the times at which thephase of the fundamental of the voltage generated by the inverter isequal to $\frac{k\quad\pi}{p},$k being an integer. This is because it has been observed thatrelationships (14) and (15) are simpler to express and therefore tocalculate at these precise regulation times. In particular, the valuesof the parameters ε(0) and δ(0) are independent of when these timesoccur.

Here, for example, the values of these parameters ε(0) and δ(0) arecalculated by simulating a numerical model of the motor 4 and of theinverter 8. To be more precise, an operation 84 simulates the powersupply of the motor 4 with the aid of the pulse width modulation definedby the angles ail stored in the memory 32. The three-phase voltagegenerated by the model is then analyzed and the value of the amplitudeof, for example, the first 2000 voltage harmonics with an order greaterthan two is measured. With the aid of these 2000 values and the aboverelationships (14) and (15), the values of the parameters ε(0) and δ(0)are calculated for the pulse width modulation defined by the angles ail.At the end of the operation 84, a normalized value of the parametersε(0) and δ(0) calculated in this way is recorded in the table TP of thememory 32, on the row corresponding to the angles α_(i1). The normalizedvalue of ε(0) and δ(0) is obtained when dividing them by the value{circumflex over (V)}_(M).

The operation 84 is then repeated for each type of modulation defined inthe table TP of the memory 32. At the end of the phase 80, the values ofthe parameters ε(0) and δ(0) defined for each type of modulation arethus recorded in the memory 32.

Once the values of all the parameters needed for running the system 2have been recorded, the regulation phase 82 can begin.

During the regulation phase, the system 2 receives the value of the setpoint Γ_(cm) during an operation 90. This set point Γ_(cm) is, forexample, delivered by an operator or by a feedback control device (notshown). The value of this set point Γ_(cm) generally varies slowly withrespect to the frequency at which a new instantaneous current set point(Î_(d), Î_(q)) is delivered to the module 24.

At each regulation time, the unit 22 calculates a new instantaneouscurrent set point ad (Î_(d), Î_(q)) during a step 92. This new set point(Î_(d), Î_(q)) is applied to the input of the control unit 20.

From the current regulation time until the next regulation time, theunit 20 controls the inverter 8 as a function of this instantaneouscurrent set point during a step 94. The instantaneous current set pointremains constant between two regulation times.

To be more precise, during an operation 96 at the current regulationtime, the module 24 establishes the values of the angle β₀ and of themodulus ∥{right arrow over (V)}∥ which make it possible to obtain theinstantaneous torque corresponding to the instantaneous current setpoint (Î_(d), Î_(q)) as soon as the next regulation time.

The angle β₀ of the voltage vector V established by the module 24 istransmitted directly to the module 26, whereas the modulus ∥{right arrowover (V)}∥ of this same vector is transmitted to the selection module28.

During an operation 98, the module 28 selects the values of the anglesai and the values of the parameters ε(0) and δ(0) corresponding to thevalue of the modulus ∥{right arrow over (V)}∥. The recorded values ofthe parameters ε(0) and δ(0) are multiplied by the value {circumflexover (V)}_(M) measured at this time.

The selected values of the angles α_(i) are transmitted to the module26, whereas the non-normalized values of the parameters ε(0) and δ(0)are transmitted respectively to the modules 52 and 54.

With the aid of the angle β₀ and of the values of the angles α_(i),during an operation 100, the module 26 controls the switching of theswitches of the inverter 8 by using a synchronous pulse width modulationprocess.

Under the control of the module 26, the inverter 8 generates a voltageand a current corresponding to the modulus ∥{right arrow over (V)}∥ andto the angle β₀. By constructing this modulus∥{right arrow over (V)}∥and the angle β₀, the instantaneous torque of the motor reaches theinstantaneous torque set point corresponding to the input set point(Î_(d), Î_(q)) exactly at the next regulation time. This is what isrepresented on the graph in FIG. 4. The first six regulation times T₁ toT₆ have been represented on this graph. The thin horizontal linerepresents the instantaneous torque set point corresponding to the setpoint (Î_(d), Î_(q)). The bold line represents the development of theinstantaneous torque Γ, as a function of time. It may be noted that byvirtue of the operation 96, the instantaneous torque is equal to theinstantaneous torque set point at each regulation time. It may also benoted that the average of the instantaneous torque, represented by abroken horizontal line, between two regulation times is, for example,lower on this graph than the instantaneous torque set point valuecorresponding to the set point (Î_(d), Î_(q)). This explains why, as inthe known methods, if the input set point of the module 24 isestablished only from the average torque set point Γ_(cm), thedifference between the average of the instantaneous set point betweentwo regulation times and the average torque set point since thisdifference is not only a function of the average torque set point.

In order to resolve this problem, the method of FIG. 2 includes a step110 of determining the values of the current and voltage harmonics, andthe step 92 includes specific calculation operations which will now bedescribed.

During the step 110, the module 52 determines the values of thecomponents ΔI_(q) and ΔI_(d) at each regulation time, during anoperation 112, from:

-   -   the value of the angle β₀ delivered by the module 24,    -   the value of the parameter ε(0) delivered by the module 28,    -   the value of the angle ρ₀ measured by the sensor 56, and    -   the value of the angular velocity ω measured by the sensor 58.

The values determined during this operation 112 are then transmitted tothe modules 42 and 44 of the calculation unit 22.

Simultaneously with the operation 112, the module 54 determines thevalues of the components ΔJ_(q) and ΔJ_(d) during an operation 114. Thevalues of ΔJ_(q) and ΔJ_(d) are transmitted to the module 44.

In order to make it possible to obtain, from the average torque setpoint Γ_(cm), an instantaneous torque set point allowing the averagetorque set point Γ_(cm) to be reached within a few regulation times, thestep 92 includes the following operations:

-   -   an operation 120 of calculating the set point Ĩ_(q) by the        module 40, and    -   an operation 122 of correcting this set point Ĩ_(q) in order to        obtain the component Î_(q) of the instantaneous current set        point making it possible to converge the average of the        instantaneous torque between two regulation times toward the set        point Γ_(cm).

So as to take limitations of the instantaneous voltage {circumflex over(V)}_(M) and instantaneous current Î_(M) of the inverter 8 into account,during an operation 124 the module 44 establishes the value of thecomponent Î_(d) allowing these limits to be complied with.

If the set point Γ_(cm) increases, for example, then the fundamentalcurrent set point Ĩ_(q) and the instantaneous current set point (Î_(d),Î_(q)) will increase and, after the operations 122, 124 and 96, thisleads to an increase in the modulus ∥{right arrow over (V)}∥. Forexample, this increase in the modulus ∥{right arrow over (V)}∥ causesthe module 28 to select a new type of pulse width modulationcorresponding to new values for the angles α_(i). The selection of a newtype of pulse width modulation also leads to generation of differentvalues for the parameters ε(0) and δ(0). From the new values of theseparameters ε(0) and δ(0), the modules 52 and 54 determine the new valuesof the components ΔI_(q), ΔI_(d), ΔJ_(q) and ΔJ_(d) when next carryingout the operation 120, making it possible to correct the instantaneouscurrent set point (Î_(q), Î_(d)), for example by increasing it, so thatthe average of the instantaneous torque between two regulation times isequal to the set point Γ_(cm).

The method of FIG. 3 thus makes it possible to regulate the averagetorque of the motor by using an exact response control process. Ittherefore has a wide dynamic range. Furthermore, the exact responsecontrol process is combined with a synchronous pulse width modulationprocess in this case, so that certain specific harmonic orders areeliminated.

As a variant, if the computation power is sufficient, the operations122, 124, 96 and 98 are repeated multiply at each regulation time,before the operation 100 is carried out. The multiple repetition of theoperations 122, 124, 96 and 98 makes it possible to obtain a moreprecise value for the current set point (Î_(d), Î_(q)). Thus, if thenumber of iterations is large enough, the set point (Î_(d), Î_(q)) issufficiently precise to make it possible to reach any new value of theaverage torque set point Γ_(cm), which is itself in rapid variation,after just one regulation time.

The system 2 has been described here with reference to the particularcase in which the exact response control operation is carried outaccording to the teaching of application EP-A-123 35 06. As a variant,however, another exact response control method may be used, for examplea method based on so-called sliding modes.

1. A method for regulating the average electromagnetic torque of apolyphase rotating electrical machine equipped with stator and/or rotorwindings, which are supplied with a polyphase voltage and a polyphasecurrent that are generated by an inverter, the inverter being formed byswitches whose switching is controllable, this method including: acontrol step (94) of switching the switches as a function of aninstantaneous torque set point, using an exact response control processto do this so that the instantaneous torque set point is reached as soonas the next regulation time, and a step (92) at each regulation time ofcalculating, from an average torque set point, the instantaneous torqueset point to be applied so that the average of the instantaneouselectromagnetic torque of the machine converges toward said averagetorque set point, which method includes a step (110) of determining thevalue of the harmonics of the voltage and/or the current which aregenerated by the inverter, and wherein the instantaneous torque setpoint is also established (at 122, 124) during the calculation step as afunction of this value of the harmonics, so as to produce aninstantaneous torque set point suitable for limiting the differencebetween the average of the instantaneous electromagnetic torque, betweentwo successive regulation times, and said average torque set point. 2.The method as claimed in claim 1, wherein the exact response controlprocess establishes (at 96) a set point for controlling the switches bypulse width modulation, and wherein the control step (94) also includesa control operation (100) of switching the switches between eachregulation time, employing a pulse width modulation process configuredas a function of said control set point established by the exactresponse control process.
 3. The method as claimed in claim 1, whereinthe pulse width modulation process is a pulse width modulation processsynchronous with the frequency of the fundamental of the voltagegenerated by the inverter, and wherein the regulation times are spacedapart by a time interval equal to T′/2p, where p is the number of phasesof the machine and T′ is the period of the fundamental of the voltagegenerated by the inverter.
 4. The method as claimed in claim 3, whereinthe exact response control process is adapted so that the phase of thefundamental of the voltage generated by the inverter at the regulationtimes is equal to $\frac{k\quad\pi}{p},$ k being an integer.
 5. Themethod as claimed in claim 1, wherein the value of the harmonics isestablished, during the determination step (110), from the value of thecontrol set point established by the exact response control process atthe preceding regulation time.
 6. The method as claimed in claim 2,wherein: the pulse width modulation process successively uses aplurality of different pulse width modulations over time, the value ofthe harmonics is established from at least one calculation parameter(ε(0), δ(0)), the various values of the or each parameter beingcalculated in advance and prerecorded (at 80) for each different pulsewidth modulation liable to be used, and the value of the or eachparameter to be used during the determination step (110) is selected (at98) as a function of the value of the control set point established bythe exact response control process (at 96) at the preceding regulationtime.
 7. The method as claimed in claim 6, wherein a calculationparameter is defined by the following relationship:${ɛ(0)} = \left( {\sum\limits_{n = 2}^{\infty}\frac{V_{n}}{n}} \right)_{0}$where: V_(n) is the amplitude of the voltage harmonic of order n, n isan integer corresponding to the order of the harmonic.
 8. The method asclaimed in claim 7, wherein the control set point is a voltage vectordefined, in an orthonormal reference frame α,β which is fixed withrespect to the stator windings, by its modulus (∥{right arrow over(V)}∥) and an angle (β₀), and in that the value of the current harmonicsis established from the following relationship:${\Delta\quad I_{q}} = {{- \frac{ɛ(0)}{L \cdot \omega}} \cdot {\cos\left( {\beta_{0} - \rho_{0}} \right)}}$where: L is the stator inductance of the rotating electrical machine, ωis the angular velocity of the rotor of the rotating electrical machine,β₀ is the angle of the voltage vector established (at 96) at thepreceding regulation time by the exact response control process, ΔI_(q)is the value of the current harmonics along the axis q in a rotatingreference frame d,q associated with the rotor flux, the rotor flux beingaligned with the axis d, and ρ₀ is the angle of the reference frame d,qwith respect to the fixed reference frame α,β associated with the statorwindings.
 9. The method as claimed in claim 8, wherein a calculationparameter is defined by the following relationship:${\delta(0)} = \left( {\sum\limits_{n = 2}^{\infty}V_{n}} \right)$ whereVn is the amplitude of the voltage harmonic of order n.
 10. The methodas claimed in claim 9, wherein the inverter is supplied from at leastone amplitude-limited direct current supply voltage, and wherein theinstantaneous torque set point is also established (at 124) during thecalculation step (92) as a function of the instantaneous value({circumflex over (V)}_(M)) of the direct current voltage available atthe regulation time, so that the instantaneous torque set pointcorresponds to an available direct current voltage.
 11. The method asclaimed in claim 10, wherein the instantaneous torque set point isestablished in the form of an instantaneous current set point (Î_(d),Î_(q)) with the aid of the following relationships:${\left\lbrack {{\hat{I}}_{d} - {\hat{I}}_{dc}} \right\rbrack^{2} + \left\lbrack {{\hat{I}}_{q} - {\hat{I}}_{qc}} \right\rbrack^{2}} \leq \frac{{\hat{V}}_{M}^{2}}{Z^{2}}$Î_(d)² + Î_(q)² ≤ Î_(M)² where: {circumflex over (V)}_(M) is theinstantaneous value of the maximum direct current voltage available forsupplying the inverter (8), Î_(M) is the instantaneous value of themaximum current that can be generated by the inverter 8, Î_(q) and Î_(d)are the components of the set point of the instantaneous current vectorrespectively along the axes q and d of the reference frame d,q Z isdefined by the following relationship: Z={square root}{square root over(R²+L²·ω²)}, where R is the stator resistance of the machine, L is thestator inductance of the machine and o) is the angular velocity of therotor of the machine, Î_(dc) and Î_(qc) are defined by the followingrelationships:${\hat{I}}_{dc} = {{- \frac{L \cdot \omega}{Z^{2}}} \cdot \left\{ {{R \cdot \left( {{\Delta\quad I_{q}} - {\Delta\quad J_{q}}} \right)} - {L \cdot \omega \cdot \left( {{\Delta\quad I_{d}} - {\Delta\quad J_{d}}} \right)} + {\omega \cdot \Phi_{a}}} \right\}}$${\hat{I}}_{qc} = {{- \frac{1}{Z^{2}}} \cdot \left\{ {{R \cdot \omega \cdot \phi_{a}} - {R \cdot L \cdot \omega \cdot \left( {{\Delta\quad I_{d}} - {\Delta\quad J_{d}}} \right)} - {L^{2} \cdot \omega^{2} \cdot \left( {{\Delta\quad I_{q}} - {\Delta\quad J_{d}}} \right)}} \right\}}$where: ΔI_(d) and ΔI_(q) are the components of the harmonic currentvector generated by the inverter (8), respectively along the axes d andq of the reference frame d,q, and ΔJ_(q) and ΔJ_(d) are componentsproportional to the harmonic voltage vector generated by the inverter,respectively along the axes q and d of the reference frame d,q, thecomponents ΔI_(d), ΔJ_(q) and ΔJ_(d) being defined by the followingrelationships:${\Delta\quad I_{d}} = {{+ \frac{ɛ(0)}{L \cdot \omega}} \cdot {\sin\left( {\beta_{0} - \rho_{0}} \right)}}$${\Delta\quad J_{d}} = {\frac{\delta(0)}{L \cdot \omega} \cdot {\sin\left( {\beta_{0} - \rho_{0}} \right)}}$${\Delta\quad J_{q}} = {{- \frac{\delta(0)}{L \cdot \omega}} \cdot {\cos\left( {\beta_{0} - \rho_{0}} \right)}}$12. An information storage medium (60), which includes instructions forcarrying out a regulation method as claimed in claim 1, when saidinstructions are carried out by an electronic computer.
 13. A datastructure stored in a memory (32), capable of making it possible toregulate the average electromagnetic torque of a polyphase rotatingelectrical machine (4) when it is used in a method as claimed in claim1, which data structure associates a plurality of angles (α_(i)) and thevalue of at least one regulation parameter (ε(0), δ(0)) with eachparticular value of a control set point (∥{right arrow over (V)}∥)established by the exact response control process, the set of angles(α_(i)) associated with a given value of said control set point defininga particular pulse width modulation synchronous with the frequency ofthe fundamental of the voltage generated by the inverter (8), and thevalue of said at least one regulation parameter (ε(0), δ(0)) being afunction of the value of the current and/or voltage harmonics which aregenerated by the inverter, when it is controlled with the aid of thepulse width modulation defined by the angles (α_(i)) associated with thesame value of the control set point (∥{right arrow over (V)}∥).
 14. Asystem for regulating the average electromagnetic torque of a polyphaserotating electrical machine equipped with stator and/or rotor windings,which are supplied with a polyphase voltage and a polyphase current thatare generated by an inverter (8), the inverter being formed by switcheswhose switching is controllable, this system including: a control unit(20) for the switching of the switches as a function of an instantaneoustorque set point, this control unit being capable of using an exactresponse control process to do this so that the instantaneous torque setpoint is reached as soon as the next regulation time, and a unit (22)for calculating, from an average torque set point, the instantaneoustorque set point to be applied so that the average of the instantaneouselectromagnetic torque of the machine (4) converges toward said averagetorque set point, which system includes a unit (50) for determining thevalue of the harmonics of the voltage and/or the current which aregenerated by the inverter (8), and wherein the calculation unit (22)also calculates the instantaneous torque set point as a function of thisvalue of the harmonics, so as to produce an instantaneous torque setpoint suitable for limiting the difference between the average of theinstantaneous electromagnetic torque, between two successive regulationtimes, and said average torque set point.